Mirror clips are made for exactly this purpose. Plain or fancy as fits your decor and/or budget.

If that mirror has a wooden frame you can attach picture hanging brackets.

the frame looks to be about 10mm thick which is plenty.

If the mirror doesn't weigh much more than 15 pounds, you could use some Command picture hanging strips (such as these or these). They're easy to install and relatively inexpensive.

Another option is a french cleat. You really, really, don't want mirrors to fall off the wall. They shatter and explode and if there is any biological unit in the area they are likely to get cut (not to mention any heart attacks from the explosion or the seven years bad luck).

You can buy one (e.g.: https://www.amazon.com/Hangman-Z-Hanger-Mirror-Picture-Aluminum/dp/B002NEFF7Y/ref=asc_df_B002NEFF7Y/?tag=hyprod-20&linkCode=df0&hvadid=198097826602&hvpos=1o3&hvnetw=g&hvrand=16069312577621920230&hvpone=&hvptwo=&hvqmt=&hvdev=c&hvdvcmdl=&hvlocint=&hvlocphy=9031347&hvtargid=aud-801381245258:pla-321036497668&psc=1)

Or make one from a piece of wood: https://www.instructables.com/id/French-Cleat/

If you do make one from wood, you'll probably need either two (top and bottom of mirror) or a bolster at the bottom if you want the mirror to hang parallel with the wall. Sometimes having the mirror angled slightly down is desired.

I mounted a similar mirror to a wall by drilling symmetrically-spaced holes through the frame (about one per six inches of frame perimeter) and screwing the mirror directly to the drywall using appropriate-length black phosphate coarse thread drywall screws.

In my case the the holes in the frame were acceptable, and due to the dark red-brown color of the frame the black screw heads were all but invisible. (Spacing them carefully also helped reduce the visual impact, and I believe I placed them in a valley in the molding profile to further hide them.)

When doing it this way you gain the opportunity to align either the center or one side of the mirror over a stud, and use appropriate-length longer screws to get extra holding strength at the stud.

Screws

You might consider double headed nails or screws. I like screws, since nails can work out of the wall.

The link below would be a good style, and the last pic shows exactly how it would work with your mirror. This style also allows for adding D-rings, wire, or sawtooth hangers (even though the "artist" is wrong about the orientation of the sawtooth hanger as well as what a keyhole looks like). With your mirror, you can even use this style bare, although it would have a tendency to walk off the head and it would damage the paper backing.

I'm only suggesting these specific screws because they have a nice long shank between the heads. I'm sure the OP can find similar ones at a different retailers. Also, the variety of images in this listing are useful.

https://www.amazon.com/dp/B07RQWQP5Q/ref=sspa_dk_detail_8?psc=1&spLa=ZW5jcnlwdGVkUXVhbGlmaWVyPUEyVUtYNlVLODFLOEw0JmVuY3J5cHRlZElkPUEwNzI1NDAxQU1CWk9aNk1HNjRRJmVuY3J5cHRlZEFkSWQ9QTA0NjA2NTMxV1JMM1dFRFlOTEs0JndpZGdldE5hbWU9c3BfZGV0YWlsMiZhY3Rpb249Y2xpY2tSZWRpcmVjdCZkb05vdExvZ0NsaWNrPXRydWU=

You can add D-rings without too much trouble and, with a pilot hole, without splitting the frame. Using screws will prevent damaging the frame and the mirror from shattering that a hammer and nails would almost guarantee. Adding a wire is almost a guarantee it won't be straight, and adding sawtooth hangers is definitely a guarantee of it being crooked, unless you add two of them. Usually sawtooth hangers are attached by nails, as I've already warned against.

Hooks

You can also try hooks like these, but they might also allow the mirror to walk off the end and would damage the paper backing. These can also be used with D-rings and wires, but generally not with sawtooth hangers.

Mirror clips come in many thickness sizes. Choose one with adequate gap to mirror and use _|— to fasten with exposed screw, but allow mirror to be flush. Use a small < 1cm square double sided tape in middle if it bulges out but permits removal.

Mirrors are often mounted simply using double-sided adhesive tape. Just google "adhesive tape mirror", and you'll find a lot of products from all brands. You'll find those in your local depot, too.

Just be aware that there are two kind of double-sided tape: one that is very thin, and one that is thicker (~2mm), with a core made of foam. If the wall surface isn't perfectly smooth (e.g. a drywall painted with a roller typically isn't smooth enough), you need to use the foam type.

Also, be aware that, if you ever plan to remove the mirror, the tape may be strong enough that you can't just unstick it without risking breaking it.

You could use a shelf with a ledge on the end like this:

or possibly

amazon link

to secure the mirror.

You can get mirror brackets/clips intended specifically for this use. Here are two examples:

(of course, you need to get ones in a matching color and texture or color them yourself etc.)

As for placing them, you have multiple options:

1. One bracket at the center of each of the four sides of the mirror (top, bottom, left, right)


2. Two brackets at 1/5 and 4/5 of the bottom and the top (or even closer to the left and right edges)


3. Two brackets at the bottom and the top + two brackets at 1/2 of the left and right sides.


4. Some brackets are intended for corners; in that case it's one at each of the four corners.


5. etc. etc.

Here's an example of option 2: